The talent series starts with the three Pegasus books and continues through the Tower and Hive books. Nobody seems to be continuing the series since Anne passed away.

jjs, I assume you're looking for stories where humans have various psychic abilities, like telepathy, precognition, clairvoyance, and telekinesis. There are plenty of short stories and one-off novels in this genre. Some that I've read are:

The Barque cats are unusually intelligent cats that are trained to hunt rats in the ducts of spaceships and warn the humans about air-leakages. They acquire telepathic powers (with one human apiece) through contact with a mysterious substance disseminated by a -- SPOILER ALERT!

The one-on-one telepathic connection is akin to the relationship between humans and dragons on Pern. So it's not really similar to the Talent series.

You might like the Elemental Masters series by Mercedes Lackey. Most of the books have to do with "mages" who can draw magic power from elemental spirits of Air, Fire, Earth, or Water. One book at least (The Wizard of London) deals with a school for children with Talents (such as telepathy, precognition, clairaudience, psychometry, etc.) rather than Magic.

I wouldn't have thought of those books as a comparison to the Pegasus/Tower books, but I do recommend them as one of my favorite series! It's excellent historical fiction, revealing magic behind the scenes, and the faint framework of a traditional fairy tale behind that. (Some of those are more obvious than others...)
The first book is "The Serpent's Shadow".

The 2 main children in Wizard of London each have a telepathic (or empathic) connection with a bird, which protects its chosen girl --- so maybe a bit like Barque cats or fire-lizards. Can't think of one off-hand that is mainly about moving cargo over huge distances by telekinesis.

And I don't know how similar jjs wanted the series to be to Anne's Talents universe. Too similar, and the author could get sued for plagiarism. Most of the ones I suggested are even less similar to the Talents series.

If you want something to do with psy gifts, you must read : The Galactic Milieu Serie, by Julian May. The first one "Intervention" is like Pegasus. And the trilogy that follows is more like Tower. You will enjoy it !